1. Field of the Invention
Embodiments of the present invention generally relate to techniques for processing seismic data and, more particularly, to removing noise and aliased energy in the tau-P domain for successful interpolation of seismic gathers.
2. Description of the Related Art
In the oil and gas industry, seismic surveys are one of the most important techniques for discovering the presence of subterranean hydrocarbon deposits. If the data is properly processed and interpreted, a seismic survey can provide geologists with a two-dimensional (2-D) or three-dimensional (3-D) representation of subsurface lithologic formations and other features, so that they may better identify those formations likely to contain oil and/or gas. Having an accurate representation of an area's subsurface lithologic formations can increase the odds of hitting an economically recoverable reservoir when drilling and decrease the odds of wasting money and effort on a nonproductive well.
A seismic survey is conducted by deploying an array of energy sources and an array of receivers in an area of interest. Typically, vibrator trucks are used as sources for land surveys, and air guns are used for marine surveys. The sources are discharged in a predetermined sequence, sending a downgoing seismic wavefield or signal into the earth that is partially reflected by subsurface seismic reflectors (i.e., interfaces between subsurface lithologic or fluid units having different elastic properties). The reflected or upgoing wavefield or signals (known as “seismic reflections”) are then detected and converted to electrical signals by the array of receivers located at or near the surface of the earth, at or near the water surface, or at or near the seafloor. Each receiver records the amplitude of the incoming signals over time at the receiver's particular location, thereby generating a seismic survey of the subsurface. The seismic energy recorded by each seismic receiver for each source activation during data acquisition is generally referred to as a “trace.” The seismic receivers utilized in such operations typically include pressure sensors, such as hydrophones, and velocity sensors, such as single or multi-component geophones. Since the physical location of the sources and receivers is known, the time it takes for a reflection wave to travel from a source to a sensor is directly related to the depth of the formation that caused the reflection. Thus, the recorded signals, or seismic energy data, from the array of receivers can be analyzed to yield valuable information about the depth and arrangement of the subsurface formations, some of which hopefully contain oil or gas accumulations.
This analysis typically begins by organizing the data from the array of receivers into common geometry gathers, where data from a number of receivers that share a common geometry are analyzed together. A gather will provide information about a particular location or profile in the area being surveyed. Ultimately, the data will be organized into many different gathers and processed before the analysis is completed in an effort to map the entire survey area. The types of gathers typically employed include common midpoint (i.e., the receivers and their respective sources share a common midpoint), common source (i.e., the receivers share a common source), common offset (i.e., the receivers and their respective sources have the same separation or “offset”), and common receiver (i.e., a number of sources share a common receiver). Common midpoint gathers are the most common type of gather at present because they allow the measurement of a single point on a reflective subsurface feature from multiple source-receiver pairs, thus increasing the accuracy of the depth calculated for that feature.
The data in a gather is typically recorded or first assembled in the time-offset domain. That is, the seismic traces recorded in the gather are assembled or displayed together as a function of offset (i.e., the distance of the receiver from a reference point) and of time. The time required for a given signal to reach and be detected by successive receivers is a function of its velocity and the distance traveled. Those functions are referred to as kinematic travel time trajectories. Thus, at least in theory, when the gathered data is displayed in the time-offset domain (the T-X domain), the amplitude peaks corresponding to reflection signals detected at the receivers should align into patterns that mirror the kinematic travel time trajectories. It is from those trajectories that one ultimately may determine an estimate of the depths at which formations exist.
A number of factors, however, make the practice of seismology and, especially, the interpretation of seismic data much more complicated than its basic principles. Primarily, the upgoing reflected signals that indicate the presence of subsurface lithologic formations are typically inundated with various types of noise. The most meaningful signals are the so-called primary reflection signals, those signals that travel down to the reflective surface and then back up to a receiver. When a source is discharged, however, a portion of the signal travels directly to receivers without reflecting off of any subsurface features. In addition, a signal may bounce off of a subsurface feature, bounce off the surface, and then bounce off the same or another subsurface feature, one or more times, creating so-called multiple reflection signals. Other portions of the detected signal may be noise from ground roll, refractions, and unresolvable scattered events. Some noise, both random and coherent, may be generated by natural and man-made events outside the control of the survey, such as wind noise.
All of this noise is detected along with the reflection signals that indicate subsurface features. Thus, the noise and reflection signals tend to overlap when the survey data are displayed in T-X space. The overlap can mask primary reflection signals, the so-called seismic events, and make it difficult or impossible to identify patterns in the display upon which inferences about subsurface geological strata may be drawn. Accordingly, various mathematical methods have been developed to process seismic data in such a way that noise is separated from primary reflection signals.
Many such methods seek to achieve a separation of signal and noise by transforming the data from the T-X domain to other domains, such as the frequency-wavenumber (F-K) or the time-slowness (tau-P) domains, where there is less overlap between the signal and noise data. Once the data is transformed, various mathematical filters are employed to the transformed data to eliminate as much of the noise as possible in an effort to enhance the primary reflection signals. The data is then inverse transformed back into the T-X domain for interpretation or further processing. For example, so-called Radon filters are commonly used to attenuate or remove multiple reflection signals. Such methods rely on Radon transformation equations to transform data from the T-X domain to the tau-P domain where it can be filtered. More specifically, the T-X data is transformed along kinematic travel time trajectories having constant velocities and slownesses, where slowness p is defined as the reciprocal of velocity (p=1/v).
The main problem with the tau-P interpolation is the presence of aliased energy in the tau-P domain. If left unchecked, the aliased energy may lead to high noise levels on the output where the tau-P data has been inverse transformed back into the T-X domain, rendering the tau-P technique unusable. One method to manage the aliased energy is the so-called high resolution Radon transform. In the high resolution Radon transform, the transform domain is forced to be maximally sparse, thereby eliminating the spurious aliased energy. Fast algorithms for high resolution 2-D Radon transforms exist and are known to those skilled in the art. However, these fast algorithms cannot be readily extended to three dimensions since the matrix structure does not have the required properties.
Accordingly, what is needed are techniques for dealing with aliasing noise in 3-D tau-P interpolation.